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A natural Monte Carlo method to approximate conditional expectations in aprobabilistic framework is justified by a general result inspired on theBesicovitch covering theorem on differentiation of measures. The method isspecially useful when densities are not available or are not easy to compute.The method is illustrated by means of some examples and can also be used in astatistical setting to approximate the conditional expectation given asufficient statistic, for instance. In fact, it is applied to evaluate theminimum risk equivariant estimator (MRE) of the location parameter of a generalhalf-normal distribution since this estimator is described in terms of aconditional expectation for known values of the location and scale parameters.For the sake of completeness, an explicit expression of the the minimum riskequivariant estimator of the scale parameter is given. For all we know, theseestimators have not been given before in the literature. Simulation studies arerealized to compare the behavior of these estimators with that of maximumlikelihood and unbiased estimators.

A Monte Carlo Method to Approximate Conditional Expectations based on a  Theorem of Besicovitch: Application to Equivariant Estimation of the  Parameters of the General Half-Normal Distribution